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Three Roads To Quantum Gravity

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CHAPTER 13<br />

............................................................................................<br />

HOW TO WEAVE A STRING<br />

Perhaps the main reason why some physicists do not get very<br />

excited about loop quantum gravity is that, although it<br />

succeeds very well in describing how the geometry of space<br />

must look on the Planck scale, it is basically pretty boring.<br />

There are no new principles involved. <strong>To</strong> set up the theory we<br />

just put in the basic principles of quantum theory and<br />

relativity. We get a lot out that is new and could even be<br />

tested experimentally. But it is perhaps not so surprising that<br />

when geometry is treated quantum theoretically it behaves<br />

like a quantum theoretic system. Things that used to be<br />

continuous, such as the range of possible volumes a space<br />

could have, now become discrete. The main lesson is that we<br />

really can treat space and time in a background independent<br />

way, and see them as a nothing but a network of relationships.<br />

This is good, but this is also what the principles we put in<br />

demanded. That it works is a good consistency check, but we<br />

should not consider it either surprising or revolutionary. The<br />

main strength of this approach, its simplicity and transparency,<br />

is perhaps also its main weakness.<br />

String theory is just the opposite. We start not with basic<br />

principles, but by contradicting the thing we feel most certain<br />

about quantum gravity ± that it must be a background<br />

independent theory. We ignore this, and search for a theory<br />

of gravitons and other particles moving against a background<br />

of empty space; and, by trial and error, we ®nd it. Our guiding<br />

principle is to ®nd something that works. <strong>To</strong> do this we have

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